We look at the division of 642553 by 89 
We want to divide 642553 by 89.

Going ahead to step 1:
89 goes into 6 0 times with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Grab the next digit (4) from the dividend, add it to 6, then carry on: 64 / 89

Step 2:
When dividing 64 by 89, we get 0 with a remainder of 64.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 64, we get 64.
Append the next digit (2) from the dividend to 64 and continue with: 642 / 89

Moving on to step 3:
If we divide 642 by 89, we get 7 and a remainder of 19.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
If we subtract 623 from 642, we get 19.
Include the next digit (5) from the dividend after 19, then repeat: 195 / 89

On to step 4:
The number 89 fits into 195 2 times, leaving a remainder of 17.
The number 2 becomes the next digit in our result. 
Result so far: 72.0
Subtracting 178 from 195 leaves us with 17.
Bring next digit (5) of the dividend behind the 17 and repeat the process: 175 / 89

Moving on to step 5:
89 can be fit into 175 1 times, resulting in a remainder of 86.
The next digit of our result is 1. 
Result so far: 721.0
The remainder is 86 after subtracting 89 from 175.
Append the next digit (3) from the dividend to 86 and continue with: 863 / 89

Advancing to step 6:
863 divided by 89 is 9 with a remainder of 62.
Record the quotient 9 as the next digit in the result. 
Result so far: 7219.0
Subtracting 801 from 863 leaves us with 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Moving on to step 7:
620 divided by 89 is 6 with a remainder of 86.
Use 6 as the next digit of our solution. 
Result so far: 7219.6
If we subtract 534 from 620, we get 86.
Since there are no more digits in the dividend, we add a zero to the remainder making it 860, and continue the process.

Going ahead to step 8:
When dividing 860 by 89, we get 9 with a remainder of 59.
Put 9 as the next digit of the answer. 
Result so far: 7219.69
If we subtract 801 from 860, we get 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

On to step 9:
If we divide 590 by 89, we get 6 and a remainder of 56.
The next digit of our result is 6. 
Result so far: 7219.696
Subtracting 534 from 590 leaves us with 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Let's proceed to step 10:
The number 89 fits into 560 6 times, leaving a remainder of 26.
The next digit of our result is 6. 
Result so far: 7219.6966
Subtract 534 from 560 to get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

The quotient of the division is 7219.6966, and the remainder is 0.00026.